Computer GraphicsGlobal Illumination:

Photon Mapping, Participating Media

Lecture 12Taku Komura

2

last lecture

Monte-Carlo Ray Tracing Path Tracing Bidirectional Path Tracing

Photon Mapping

3

Today

Methods to accelerate the accuracy of photon mapping

Rendering Participating Media

Accelerating the accuracy of photon mapping

Combine with ray tracing to visualize the specular light visible from the camera

Shoot more photons towards directions where more samples are needed Caustics photon map

Tracing photons only towards specular surfaces

A Practical Two-Pass Algorithm

Building photon maps by photon tracing Separate the photon paths into different

categories according to the reflectance Rendering

Combining the radiance of difference light paths

Light Transport Notation

L: Lightsource E: Eye S: Specular reflection D: Diffuse reflection (k)+ one or more k events (k)* zero or more of k events (k)? zero or one k event (k|k’) a k or k’ event

Photon Tracing

Create two photon maps Global photon map (the usual photon map)

All Photons with property L(S|D)*D are stored. Caustics photon map

Created by tracing photons that hit the specular surfaces Cast the photons only toward specular objects LS+D

Rendering

Separate the irradiance into four groups Direct illumination (by ray tracing or global

photon map) : LD Diffuse indirect illumination (by global photon

map) : LD(S|D)+D Specular reflection (by ray tracing) L(S|D)*S Caustics (by caustics photon map) LS+D

Caustics Photon Map

Caustics require high resolution Need to cast more photons towards

surfaces that generates caustics Projection Map

Projection map A map of the geometry seen from the light source

Made of many cells – which is on if there is a geometry in that direction, and off if not

For a point light, it is a spherical projection For directional light, a planar projection Use a bounding sphere to represent the objects

Direct + Indirect + Specular

Why is photon mapping efficient?

It is a stochastic approach that estimates the radiance from a few number of samples Kernel density estimation

Can actively distribute samples to important areas Caustics photon map

14

Today

Methods to accelerate the accuracy of photon mapping

Rendering Participating Media

Participating Media Dusty air, clouds, silky water Translucent materials such as marble,

skin, and plants Photon mapping is good in handling

participating media In participating media, the light is

scattered to different directions

Single / Multiple scattering

The brightness of a point

Is decided by Out scattering Absorption In scattering

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Light out-scattering

• The change in radiance, L, in the direction ω, due to out scattering is given by

• The change in radiance due to absorption is

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tcoefficien absorption: )(

tcoefficien scattering : )(

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In-scattering

• The change due to inscattering

where the incident radiance, Li, is integrated over all directions

p is called the phase function describing the distribution of the scattered light

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Phase function Isotropic scattering

Scattered in any random direction

Henyey-Greenstein Phase Function Scattered in the direction more

towards the front Dust, stone, clouds

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Phase function

Examples

Cornell Box scene – isotropic, homogeneous participating medium.

200,000 photons used with 65,000 in the volume map. Radiance

estimate used 100 photons.

Cornell Box scene – anisotropic, homogeneous participating medium.

200,000 photons used with 65,000 in the volume map. Radiance

estimate used 50 photons.

Ray marching and single scattering

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s

N

li

t

• Now we compute how the light will be accumulated along a ray

• This is called ray marching

where N is the number of light sources and Li is

the radiance from each light source

The last term is the light entering from behind, which is attenuated by proceeding Δx

Ray marching through a finite size medium (Single Scattering)

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• For multiple scattering, it is necessary to integrate all the in-scattered radiance at every segment

• Here S sample rays are used to estimate the in-scattered light

Multiple scattering

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• Photon mapping can efficiently handle multiple scattering

• The photons interact with the media and are scattered / absorbed

• The average distance the photon proceeds after each interaction is

• Here S sample rays are used to estimate the in-scattered light

Photon mapping participating media

t coefficienon terminati:

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ast

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Photon Scattering

• The photon is either absorbed or scattered• The probability of scattering is

• Deciding what happens by Russian Roulette

• Once the photon interacts with the media, it is stored in a volume photon map

t

s

absorbed isPhoton

scattered isPhoton [0,1]Given

Volume Radiance Estimate

• Same as we did for surface radiance estimate, locate n nearest photons and estimate the radiance

31

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Rendering Participating Media

• By ray tracing • If a ray enters a participating media, we use

ray marching to integrate the illumination.

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Single scattering term

multiple scattering term

Examples

single scattering multiple scattering

Subsurface Scattering• In computer graphics, reflections of non-metallic materials

are usually approximated by diffuse reflections. • Light leaving from the same location where it enters the

object• For translucent materials such as marble, skin and milk, this

is a bad approximation• The light leaves from different locations

Single scattering

Direct single scattering: Compute the distance the light has

traveled and attenuate according to the distance

Indirect Multiple scattering : Photon maps

Subsurface Scattering by Photon Mapping

• Photon tracing – as explained before• Rendering – Ray marching

BSSRDF

• Bidirectional Scattering Surface Reflectance Distribution Function (BSSRDF)

• Relates the differential reflected radiance dLr, at x in the direction ω, to the differential incident flux, dΦ, at x’ from direction ω’.

• We can capture/model the BSSRDF and use it for rendering

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Rendering using BSSRDF

(a) sampling a BRDF (b) sampling a BSSRDF Collect samples of incoming rays over an area

http://graphics.ucsd.edu/~henrik/animations/BSSRDF-SIGGRAPH-ET2001.avi

Rendering by BSSRDF

Human skin reflectance simulated by

BRDF BSSRDF

• Readings : Realistic Image Synthesis Using Photon Mapping by Henrik Wann Jensen, AK Peters Chapter 9, 10